Many times when a homeowner is granted a loan modification on the first mortgage, there may be a second mortgage or home equity loan that remains in default. The big question is what to do about this second mortgage? Typically the second mortgage has been in default for sometime and there is a resulting arrears. Many times when the first mortgage company agrees to modify, it usually will require the homeowner to start making trial payments soon thereafter so there is not much time to get the second modified. Notwithstanding, the second mortgage company typically will only modify after the first mortgage is modified anyway. Usually then the homeowner will start the trial period with the hope that the second will modify its mortgage favorably to the homeowner. If, however, the newly modified mortgage payment on the first mortgage combined with ordinary household expenses consumes most of the homeowner's monthly income then there may be nothing left over for the second mortgage, making a modification of the second mortgage unlikely. If the second mortgage company is unwilling to settle for much less than what is owed it then the second mortgage may just hang in limbo with its arrears increasing by the day--an unsettling feeling to any homeowner. However, under this situation, the second mortgage company probably won't foreclose if the first mortgage is owed an amount near the value of the house, but if the amount owed on the first mortgage is significantly less than the value of the house then the second mortgage company would need to seriously consider its right to foreclose on its second mortgage. 

It is worth mentioning that if the amount owed on the first mortgage exceeds the value of the property, the homeowner may have the ability in bankruptcy to have the second mortgage lien stripped off the property. This is the case in the 11th Circuit, but as of now, it is not the case in New York, well at least not in the Eastern District of New York.

I do not believe that NY has a "wrongful foreclosure" defense per se; however, if the bank has commenced a wrongful foreclosure in a New York court, then you will need to give specifics as to why you believe the foreclosure is wrongful. The facts supporting a wrongful foreclosure are case sensitive. For example, if the bank knowingly or negligently claimed to be the owner of the mortgage when it really wasn't, then one could assert that the bank's actions are wrongful and unconscionable; this defense must be raised or it will be lost. This would not only be a defense but could serve additionally as a counterclaim which would serve as a basis for damages. But again, they must be raised in the answer or be lost. There are some exceptions to this general rule, like if you could not have learned of the bank's wrongful conduct at the time the answer was due. In such cases, you would have to raise the defense and or counterclaim via motion soon after you discovered the wrongful conduct. 

BTW, defenses that are not waived in New York even though not raised in the answer are: the defense asserting that the complaint fails to state a cause of action, failure to name a necessary party defendant, the defense that the court lacks subject matter jurisdiction, and RPAPL 1303/1304 notice requirements---these defenses even though not raised in the formal answer can still be raised later in the litigation, but generally must be raised before judgment with the exception of the court lacks subject matter jurisdiction defense, which defense can be raised anytime even after judgment. In the above example, even if the defense of standing was not timely raised in the answer, one may still be able to argue later in the litigation that the bank's complaint fails to state a cause of action based on the fact that the bank's cause of action cannot be satisfied if it is not the holder of the subject note and mortgage.